88 lines
2.4 KiB
C
88 lines
2.4 KiB
C
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/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2011 Fredrik Johansson
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******************************************************************************/
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#include "arith.h"
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void _arith_bernoulli_number_zeta(fmpz_t num, fmpz_t den, ulong n)
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{
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mpz_t r;
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mpfr_t t, u, z, pi;
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mp_bitcnt_t prec, pi_prec;
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arith_bernoulli_number_denom(den, n);
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if (n % 2)
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{
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fmpz_set_si(num, -(n == 1));
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return;
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}
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if (n < BERNOULLI_SMALL_NUMER_LIMIT)
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{
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fmpz_set_si(num, _bernoulli_numer_small[n / 2]);
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return;
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}
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prec = arith_bernoulli_number_size(n) + fmpz_bits(den);
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prec += 10 + 2*FLINT_BIT_COUNT(n);
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pi_prec = prec;
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mpz_init(r);
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mpfr_init2(t, prec);
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mpfr_init2(u, prec);
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mpfr_init2(z, prec);
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mpfr_init2(pi, pi_prec);
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/* t = 2 * n! / (2*pi)^n */
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flint_mpz_fac_ui(r, n);
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mpfr_set_z(t, r, GMP_RNDN);
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mpfr_mul_2exp(t, t, 1, GMP_RNDN);
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mpfr_const_pi(pi, GMP_RNDN);
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mpfr_mul_2exp(pi, pi, 1, GMP_RNDN);
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mpfr_pow_ui(pi, pi, n, GMP_RNDN);
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mpfr_div(t, t, pi, GMP_RNDN);
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/* t = t / zeta(n) */
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mpfr_zeta_inv_euler_product(z, n, 0);
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mpfr_div(t, t, z, GMP_RNDN);
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/* round numerator */
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fmpz_get_mpz(r, den);
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mpfr_mul_z(t, t, r, GMP_RNDN);
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mpfr_round(t, t);
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mpfr_get_z(r, t, GMP_RNDN);
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fmpz_set_mpz(num, r);
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if (n % 4 == 0)
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fmpz_neg(num, num);
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mpz_clear(r);
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mpfr_clear(t);
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mpfr_clear(u);
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mpfr_clear(z);
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mpfr_clear(pi);
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}
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